He has been knighted by Queen Elizabeth II and rubbed elbows with the Dalai Lama. His medical work has reached 70 countries, tackling everything from tuberculosis in Peru to child mortality rates in Ghana.

But that global acclaim didn’t count for much on a recent Thursday afternoon when Don Berwick walked under a white tent in Waltham where the annual chamber of commerce barbecue was in full swing. Smoke billowed from a grill. Frank Sinatra crooned on the sound system.

This is Berwick’s challenge as he struggles to make the jump from rock star in the rarefied realm of health care quality improvement to credible contender for governor of Massachusetts.

His high-flying résumé — parts of which would fit comfortably on Bono’s list of global achievements — has not translated easily onto the ground in Lowell and Worcester.

Though his background is wider-ranging than any Democrat in the race, and though he has the most distinctive policy positions, Berwick is trailing far behind Martha Coakley and Steve Grossman. Polls show 65 percent of likely voters in Tuesday’s primary don’t even know who he is.

A rumpled 67-year-old pediatrician from Newton who does crossword puzzles before bedtime, Berwick launched the Institute for Healthcare Improvement in Cambridge in 1991. The $40 million nonprofit helps governments and hospitals around the world reduce medical errors and improve care. In 2005, he earned knighthood for helping an entire country, Britain, overhaul its troubled health care system. And from 2010 to 2011, he ran Medicare and Medicaid for President Obama.

He is the only Democrat running for governor who opposes casinos and supports single-payer health care, a seismic shift that he says would save millions of dollars by using the government, rather than private insurers, to finance the health care system.

He calls himself “the most progressive candidate in the field by far” and likes to quote Hubert Humphrey’s rubric that government needs to meet a “moral test” of how it treats those on the margins of society.

With voters, he is so soft-spoken that, even in small groups, people have to lean in to listen to him. But his quiet basso should not be confused with a lack of self-confidence.

He often talks about himself in global terms — an expert “who helped design health care delivery around the world” — and he can show flashes of frustration that the press and the broader electorate have not fully grasped the influence of his work.

“I’m the one person in the world who has said the most about how we can have absolutely all the care we want and need,” he recently told reporters, as he walked briskly along Atlantic Avenue to a fund-raiser at a downtown law office. “All we have to do is organize it properly.”

On the trail, he travels modestly, in a Honda Civic owned by David Marsh, a 23-year-old Williams College graduate who holds the official title of policy director on the campaign.

‘Part of it is being a doctor, but a lot more of it is being the kind of executive I know I can be, and what I know you can get done with that.’

Only recently did he agree to give up driving himself after Marsh and other aides convinced him he could get work done if he wasn’t behind the wheel.

Cruising on the Massachusetts Turnpike to a meeting with South Asian business executives in Boston, Berwick never mentioned the polls that showed him in third place or the latest ads his opponents were running. Instead, he and Marsh discussed the Affordable Care Act and the Israeli-Palestinian conflict.

“I’m going to e-mail you a blog posting about legal challenges to the ACA, just so we understand it,” Berwick told Marsh, who nodded.

Then Berwick raised a point that had been bothering him. A woman at a fund-raiser had reacted angrily, he said, when he mentioned that Hamas uses civilians as “human shields” to protect its rockets in Gaza. She had argued there were no human shields, he said.

Berwick asked where he could find reliable information on the issue. Marsh suggested trying a range of news outlets and tried to steer the candidate back to local concerns.

“For our purposes, that’s not a road I think we want to go down,” the aide said.

In between making fund-raising calls, Berwick eagerly courted the press — a sign of his openness and willingness to answer questions, but also a recognition that he needed every ounce of ink and second of airtime to help raise his profile with voters.

“There’s no threshold to getting through to me,” he told a WBUR reporter on the phone. “Anytime. Anywhere.”

Throughout the day, as he traveled from an interview at Channel 5 to a meeting with activists on Beacon Hill, Berwick was asked by reporters and by some of his own supporters about his lowly poll numbers. At the time, he was at single digits, and has only recently cracked 10 percent. He remained unfailingly upbeat.

“We’re on a roll,” he told a donor on the phone in Marsh’s Civic. “Winning is possible.”

Yet about a week later, on a Monday morning, the main event of his day found Berwick sitting unnoticed in the accordion-midsection of the number 28 bus as it rolled past nail salons and discount stores from Mattapan to Dudley Square. The bus ride was intended to highlight the candidate’s commitment to public transportation. But it drew little notice from the press or the traveling public.

Passengers squeezed by Berwick as he talked about “smart growth” and “modal equity” with a less-than-well-known political figure he had brought in for the occasion: Earl Blumenauer, a bow-tied congressman from Portland, Ore., who founded the Congressional Bicycle Caucus. With them was a former state transportation secretary and two young MBTA advocates.

Later, at a small fund-raiser at a downtown law office, Blumenauer handed Berwick a check for $500, saying he “exemplified the kind of people we need in government” and predicted he would surge in the polls, once voters get to know him.

“Part of the problem is that competence and accomplishment doesn’t necessarily translate into political crackle,” Blumenauer said. “But this is going to be a very low-turnout primary that is going to engage people who are a little more thoughtful, and I think that’s his sweet spot: people who think and process the information and pay attention.”

The son of a small-town doctor from Connecticut, Berwick says he always wanted to follow in his father’s footsteps. After graduating from Harvard College, the Kennedy School of Government, and Harvard Medical School, he started as a pediatrician in the Kenmore Square office of Harvard Community Health Plan in 1979.

He met the woman he would later marry, Ann Greenberg, when they were lab partners in biology class in their first week of freshman year at Harvard. She is now chairwoman of the state Department of Public Utilities.

The couple has four children: Ben, 37, a Justice Department lawyer in Washington; Dan, 35, a solar energy executive in Cambridge; Jessica, 32, a doctor who lives in Zimbabwe; and Rebecca, 27, a teacher who recently moved to Barcelona.

Berwick’s own career path shifted dramatically after Harvard Community Health Plan put him in charge of quality improvement in 1982. In the medical field, the job traditionally meant punishing doctors who made mistakes.

But Berwick took the position just as companies like Toyota were reshaping the corporate world with management theories that promised to cut costs while improving quality.

Frustrated that error rates were not dropping at his own company, Berwick met with Swissair executives, NASA scientists, and engineers at Bell Labs, looking for advice.

A. Blanton Godfrey, who was head of quality theory at Bell Labs, recalled leading Berwick on a tour and asking if there was anything he had seen that was new to him.

“He stunned me by saying, ‘I didn’t see a single thing we do today in health care,’” Godfrey said. “That was my wake-up that health care was different and a little bit behind.”

Berwick became enamored of a particular brand of management theory — “total quality management” — that seeks to enlist the entire workforce in improving quality, rather than handing that task only to managers.

In health care, that meant having hospital employees check their own work — to verify, for example, that a bed should be placed at a 45-degree angle when a patient is on a ventilator and that antibiotics should be given exactly an hour before surgery to reduce infection, said Godfrey, who became a friend and mentor.

“He didn’t invent anything per se,” said Joel I. Shalowitz, a professor of health industry management at Northwestern University, who has followed Berwick’s career. “But he drew on these management techniques and highlighted the need to do them” in the highly complex medical field, which was revolutionary in its own right.

The Institute for Healthcare Improvement expanded the work globally. It runs educational programs for nearly 200,000 health care workers across the world, and its projects include the 100,000 Lives campaign, which seeks to improve patient safety and was featured in Berwick’s first television ad.

The institute's office itself seeks to be a model of collaboration. There, Berwick made a point of eschewing the traditional chief executive’s corner office and placed his desk in a room with six other employees. He considers the institute’s work his proudest achievement, and a model for how he would govern.

“This is what I can bring to the job,” he said walking through the sleek glass space in Harvard Square.

In 2010, when Obama chose Berwick to run the Centers for Medicare & Medicaid Services, he saw it as an opportunity to bring his management ideas to a sprawling federal bureaucracy. But Republicans vowed to block his nomination, seizing on Berwick’s praise of the British-run National Health Service. (“I am romantic about the NHS; I love it,” he said in a 2008 speech.)

Republicans also portrayed Berwick as an advocate of health care rationing, pointing to a 2009 interview in which he said, “The decision is not whether or not we will ration care — the decision is whether we will ration with our eyes open.” He says the quote was taken of out of context and that he was talking about trying to shine a light on the power of insurers to restrict care.

Obama bypassed Congress and installed Berwick as a recess appointment, allowing him to run the agency for 17 months.

Berwick said he loved the job, rewrote the agency’s mission statement, and encouraged his workers to innovate, telling them, “If you fail, I will cheer you on, because it means you tried.”

But after his recess appointment ended and Berwick was effectively ousted from Washington, he returned home feeling “kind of schizophrenic,” he said. He was furious at Republicans, who he said distorted his views. But he was also yearning for another shot at public life.

“I have a strong sense that I can help,” he said. “Part of it is being a doctor, but a lot more of it is being the kind of executive I know I can be, and what I know you can get done with that. That’s a story I’d love to tell.”

He has just a few days left to tell it, and a growing sense of urgency is setting in.

At a recent Friday evening fund-raiser at a home in Cambridge, only 10 people showed up, not exactly an overflow crowd. As the guests sipped white wine, Berwick stood in the living room and spoke passionately about ending hunger and homelessness and reducing the prison population. Then he begged for help. Take a bumper sticker. Write a check. Ask two friends to write checks.